Polar Star Quantitative Commodity Fund

Dr Mauritz van den Worm, PhD

09 June, 2019

Manual vs Automated Trading

How has the increase of Automated Trading Systems (ATS) influenced the futures market?

  • CME transaction data identitifies ATS with the 1028 tag
  • Data available from November 2012 to present
  • Consider data form 2012 to 2016
  • Use gradient plots to highlight the changes
  • Graphs are interactive

MAN vs ATS - Group

MAN vs ATS - Agriculture

MAN vs ATS - Energy

Trade Participation

Where are the opportunities?

  • Limited, Local, Spectrum
    • Less liquid parts of the curve
    • Changes to macro
    • Concentrated risk on asymmetric risk/reward trades


  • Quantitative
    • Harvest systematic alpha from large universe of commodities
    • Rule based decision making process
    • Strategies inspired by discretional methodology

Literature

Grinold’s Fundamental Law of Active Portfolio Management

Law of active portfolio management

\[ \text{Performance} = \text{Skill} \times \sqrt{\text{Breadth}} \]

Suppose we are in a coin flipping casino

  • Flip coins in stead of futures
  • The coin is biased - \(P(\text{heads}) = 0.51\)

How does the betting work?

  • We have 1000 coins
  • The minimum wager is 1 coin
  • If you win you gain 1 coin
  • If you loose you loose 1 coin
  • There are 1000 tables with coin wagers
  • Games runs in parallel

What is the optimal way to allocate coins?

Two extremes

  • Bet 1000 coins on one coin flip
  • Bet 1 coin on 1000 coin flips

Expected Return

  • Single bet: \(0.51 \times 1000 + 0.49 \times (-1000) = 20\)

  • Multi bet: \(1000 \times [0.51 + 0.49 \times (-1)] = 20\)

The same expected return

Risk - Probability to lose it all:

  • Single bet: 49%

  • Multi bet: \(0.49 \times 0.49 \times \dots \times 0.49 = 0.49^{1000} \approx 0\)

Risk - Standard Deviation:

  • One coin per table

\[ \text{risk} := \text{std}\left\{1,-1,-1,1, \dots, 1 \right\} = 1 \]

  • One 1000 coin bet, 999 zero coin bets

\[ \begin{align} \text{risk} &:= \text{std}\left\{1000,0,0,0, \dots, 0 \right\} = 31.62 \\ \text{risk} &:= \text{std}\left\{-1000,0,0,0, \dots, 0 \right\} = 31.62 \end{align} \]

Coin Flip Casino - Reward/Risk

  • Just like Sharpe Ratio

  • Single bet: \(\text{SR}_{\text{single}} = \frac{20}{31.62} =0.63\)

  • Multi bet: \(\text{SR}_{\text{multiple}} = \frac{20}{1} =20\)

Coin flipping casino - Observation

  • \(20 = 0.63 \times \sqrt{1000}\)

  • \(\text{SR}_{\text{multiple}} = \text{SR}_{\text{single}} \times \sqrt{\text{Bets}}\)

  • \(\text{Performance} = \text{Skill} \times \sqrt{\text{Breadth}}\)

How does this apply to commodity futures?

  • We use insights gained from years of fundamental trading to inspire bespoke quantitative strategies that are applied to a large collection of commodity markets

  • We increase breadth or diversification by
    • how,
    • what and
    • when we trade

When we trade

What we trade

Literature

Technical considerations when trading futures systematically

  • Continuous Futures Price Series
    • We require long time series data
    • Futures expire too soon to gather sufficient data
    • How do you handle rolls?


  • Non-stationarity of Price Data
    • Time series data can only reliably be forecasted if stationary
    • Machine Learning algorithms are designed for stationary features
    • How do we create stationary data?

Continuous Futures Price Series

Continuous Futures Curves

Stationarity

Stationarity

How to obtain a stationary time series


  • Traditional
    • Price differences
    • Returns
    • Memory loss


  • Modern
    • Fractional differences
    • Memory present

Stationarity

Stationarity

Infrastructure

Core Strategies - Carry

Carry overview

  • Take advantage of curve shape
  • Contango is typically less steep in further dated contracts, i.e. it has a lower roll yield than near dated contracts
  • Extract roll yield with a short position in the near and a long position in the far dated contracts of the same commodity

Carry Example

Carry Example

Flavours of carry

  • Carry - inspired by discretionary methodology (BB1)
    • 30 commodities and 2 tenors
    • Sizing determined using percentile methodology
    • Risk 0.5% of strategy NAV per trade
    • Monthly rebalance


  • Machine Learning Enhanced Carry (BB2)
    • 30 commodities and 2 tenors
    • Fractionally differenced time-series
    • Meta labelling
    • Ensemble machine learning
    • Deterine probability of profitable trade and size trade accordingly

Backtest Assumptions

  • $10 Round trip of each contract
  • Slippage of 1 tick per contract


  • Entry cost of one spread \(= \text{\$}10 + 2 \text{ ticks} \times \text{multiplier}\)
  • Exit cost of one spread \(= \text{\$}10 + 2 \text{ ticks} \times \text{multiplier}\)

BB1 - Statistics

BB1 - Statistics

BB1 - Statistics

BB2 - Statistics

BB2 - Statistics

BB2 - Statistics

Systematic Carry - Statistics

Statistic BB1 BB1 live BB2 BB2 live
Annualized Return 5.480 3.650 19.210 8.500
Annualized Sharpe (Rf=0%) 0.662 0.542 1.239 1.878
Annualized Std Dev 8.270 6.730 15.500 4.530
Average Negative Month Return -1.608 -1.113 -2.792 -0.493
Average Positive Month Return 1.920 1.181 4.515 0.767
Maximum Drawdown 26.683 7.484 39.529 1.834
Maximum Drawdown/Annualized Return 4.869 2.051 2.058 0.216
Number of Negative Months 102.000 5.000 98.000 1.000
Number of Positive Months 149.000 8.000 151.000 10.000

Carry literature

Literature on extracting carry from futures:

Literature on applying machine learing techniques in algorithmic trading:

Core Strategies - Trend

Trend overview

  • Trend following is about absolute performance of each commodity
  • Identify trends over selection of time frames
  • Slowly build position as trend increases
  • Slowly exit position as trend decreases
  • 35 Commodities and 2 tenors

Designing, not fitting a strategy

Aim of a trend following strategy

  • Profitably trade trending markets
  • Accross a diverse universe of commodities


If we feed our trend system fake trendy data

  • linear and sinusoidal, with
  • Gaussian noise

can we trade it profitably?

Fake Trendy Data

Trend - Fake Data Performance

Trend - Statistics

Trend - Statistics

Trend - Statistics

Trend - Statistics

variable TR1 TR1 live
Annualized Return 18.930 0.310
Annualized Std Dev 17.800 16.070
Annualized Sharpe (Rf=0%) 1.064 0.019
Maximum Drawdown 26.683 9.072
Maximum Drawdown/Annualized Return 1.410 29.265
Number of Positive Months 147.000 5.000
Number of Negative Months 103.000 4.000
Average Positive Month Return 5.383 4.007
Average Negative Month Return -3.573 -4.698

Trend literature

In-house Research:

Core Strategies - Relative Roll

Relative Roll overview

Strategy not yet live.

Relative Roll literature

Core Strategies - Sentiment

Sentiment overview

Strategy not yet live.

Sentiment literature

Quantitative Portfolio

Investment Thesis

  • Focus on the intersection of technolody, data and behavioral finance applied to the broad commodity space
  • Build strategies based on sound economic theory to help deliver long-term repeatable results. Inspired by
    • academic and
    • proprietary research.
  • Investment process built on the scientific method consisting of the systematic
    • observation,
    • measurement,
    • experiment,
    • hypothesis formulation,
    • testing and
    • modification of hypothesis

Quantitative Portfolio - Statistics

Quantitative Portfolio - Statistics

Quantitative Portfolio - Statistics

Quantitative Portfolio - Statistics

Quantitative Portfolio - Statistics

Quantitative Portfolio - Statistics

Statistic 1998- 2008- 2015- live
Annualized Return 13.520 12.400 2.360 3.830
Annualized Sharpe (Rf=0%) 1.080 0.992 0.259 0.625
Annualized Std Dev 12.520 12.500 9.130 6.120
Average Negative Month Return -2.230 -2.159 -1.898 -1.295
Average Positive Month Return 3.834 3.909 2.208 1.310
Maximum Drawdown 25.575 25.575 14.132 3.995
Maximum Drawdown/Annualized Return 1.892 2.062 5.988 1.043
Number of Negative Months 113.000 64.000 26.000 5.000
Number of Positive Months 145.000 74.000 28.000 8.000

Quantitative Portfolio as supplement to S&P500

Portfolio Comparison

Statistic S&P500 PSQCF PSQCF and S&P500
Annualized Return 5.620 14.040 9.630
Annualized Sharpe (Rf=0%) 0.370 0.936 0.932
Annualized Std Dev 15.170 15.000 10.340
Average Positive Month Return 3.218 3.834 2.610
Avereage Negative Month Return -3.629 -2.230 -1.917
Number of Negative Months 100.000 112.000 102.000
Number of Positive Months 157.000 145.000 155.000
Worst Drawdown 54.029 20.216 25.903

Polar Star Multi Strategy Portfolio

Polar Star Products and S&P500

Combine Discretionary and Systematic Portfolios

Polar Star Multi Strategy as enhancement to S&P500

Portfolio Comparison

Statistic S&P500 PS Multi Strategy PS Multi Strategy and S&P500
Annualized Return 12.890 13.060 13.310
Annualized Sharpe (Rf=0%) 1.139 1.270 1.770
Annualized Std Dev 11.320 10.290 7.520
Average Positive Month Return 2.794 2.771 2.159
Avereage Negative Month Return -2.385 -1.891 -1.328
Number of Negative Months 32.000 35.000 30.000
Number of Positive Months 64.000 61.000 66.000
Worst Drawdown 17.028 6.988 7.601

Summary

Combining a

  • discretionary and
  • systematic approach

to investing in commodities we create a product with

  • positive expected return which is
  • uncorrelated to equities

that gives superior risk adjusted returns.